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Quantum Software Tools Programming

Against probability: A quantum state is more than a list of probability distributions

arXiv
Authors: Ladina Hausmann, Renato Renner

Year

2026

Paper ID

3306

Status

Preprint

Abstract Read

~2 min

Abstract Words

100

Citations

N/A

Abstract

The state ρ of a quantum system can be represented by a vector mathbf{P}_{mathcal{M}}(ρ) of outcome probabilities for a set of measurements mathcal{M}. Such representations appear throughout physics, for example, in quantum field theory via correlation functions and in quantum foundations within generalized probabilistic frameworks. In this work, we identify an unavoidable tension: to enable operationally meaningful statements, the map {ρmapsto mathbf{P}_{mathcal{M}}(ρ)} must be topologically robust unicode{x2013} preserving the notion of closeness between states. Yet, a probability representation that is topologically robust cannot simultaneously retain other essential structure, such as the subsystem structure.

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  • This paper contributes to the Quantum Software Tools & Programming research area in the Quantum Articles archive.
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  • The state ρ of a quantum system can be represented by a vector mathbfP_mathcalM(ρ) of outcome probabilities for a set of measurements mathcalM.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2601.18872 [2] arXiv https://arxiv.org/abs/2601.18872 [3] Publisher https://arxiv.org/abs/2601.18872

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